J. Phys. Chem. B 2006, 110, 4971-4977
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LiTFSI Structure and Transport in Ethylene Carbonate from Molecular Dynamics Simulations Oleg Borodin*,† and Grant D. Smith†,‡ Department of Materials Science & Engineering, Room 304, 122 South Central Campus DriVe, UniVersity of Utah, Salt Lake City, Utah 84112-0560, and Department of Chemical Engineering, UniVersity of Utah, Salt Lake City, Utah 84112 ReceiVed: October 30, 2005; In Final Form: January 10, 2006
Molecular dynamics (MD) simulations using a many-body polarizable force field were performed on ethylene carbonate (EC) doped with lithium bistrifluoromethanesulfonamide (LiTFSI) salt as a function of temperature and salt concentration. At 313 K Li+ was coordinated by 2.7-3.2 EC carbonyl oxygen atoms and 0.67-1.05 TFSI- oxygen atoms at EC:Li ) 10 and 20 salt concentrations. In completely dissociated electrolytes, however, Li+ was solvated by approximately 3.8 carbonyl oxygen atoms from EC on average. The probability of ions to participate ion aggregates decreased exponentially with an increase in the size of the aggregate. Ion and solvent self-diffusion coefficients and conductivity predicted by MD simulations were in good agreement with experiments. Approximately half of the charge was transported by charged ion aggregates with the other half carried by free (uncomplexed by counterion) ions. Investigation of the Li+ transport mechanism revealed that contribution from the Li+ diffusion together with its coordination shell to the total Li+ transport is similar to the contribution arising from Li+ exchanging solvent molecules in its first coordination shell with solvents from the outer shells.
I. Introduction Secondary (rechargeable) lithium batteries with liquid electrolytes are widely used in portable electronics and are being extensively investigated for use in environmentally friendly and efficient electric vehicles and hybrid-electric vehicles. Ethylene carbonate (EC) is one of the most commonly used solvents for mixed solvent electrolytes aimed at lithium battery applications. It has high melting point of 36.4 °C, high dielectric constant (≈90) and an acceptable viscosity (1.9 cP at 40 °C). High dielectric constant promotes ion dissociation, which is important because neutral salt aggregates and ion pairs do not carry charge and, therefore, do not contribute to charge transport, while a relatively low viscosity fosters ion diffusion as ion diffusion in liquid electrolytes have been found to be inversely proportional to solvent viscosity.1 Further lowering of the electrolyte melting point, a decrease in electrolyte viscosity, and improved low temperature performance are achieved by mixing EC with other low viscosity solvents such as dimethyl carbonate. Importantly, EC reduction products are known to form an effective solid electrolyte interphase layer on graphitic anodes that help prevent electrolyte decomposition and provide good reversibility for lithium intercalation/deintercalation. However, despite widespread use of EC in lithium batteries and a number of experimental and simulation studies of EC/Li+ interactions,2-4 the mechanism of ion transport and the nature and size of ion aggregates in EC electrolytes are still largely unknown. Molecular dynamics (MD) simulations are well suited for exploring structure and transport mechanisms in liquid electrolytes relevant to secondary lithium batteries since ions move sufficiently far on times scales accessible to MD simulations (multiple nanoseconds) to allow determination of transport † ‡
Department of Materials Science & Engineering, University of Utah. Department of Chemical Engineering, University of Utah.
properties. The lifetime of ion aggregates and solvation structure is also sufficiently short to allow equilibrium sampling on the MD time scale. However, to provide useful and reliable insight into structure and transport in these materials, the force fields employed in the simulations must capture accurately all essential physics embodied in the interactions between ions and solvent. While results from several MD simulation studies of EC,2-4 propylene carbonate (PC)5 and γ-butyrolactone (GBL)6 have been reported, most of them have considered only a single Li+ cation and have concentrated on understanding the first Li+ solvation shell. Validation of the force fields used in these simulations2,4,6 was limited to comparing the Li+ self-diffusion coefficient at infinite dilution with extrapolated experimental data. Electrolyte conductivity over wide concentration range of salt concentration was reported only in one simulation study of PC/LiBF4.5 Unfortunately, these simulations yielded a maximum conductivity of a factor of 6 lower than the experimental value revealing serious shortcomings of the simulations likely due to the force field employed. In this work we report on MD simulations of EC doped with lithium bistrifluoromethanesulfonamide (LiCF3SO2NSO2CF3 denoted at LiTFSI). TFSI- anion was chosen because it is a large anion with delocalized charge and it usually has lower binding to Li+ and yield more free (uncomplexed by anion) Li+ cations available for charge transport compared to conventional anions such as BF4-, PF6-. We utilize a recently developed accurate quantum chemistry-based many-body polarizable force field7 in order to provide a detailed picture of ion aggregation and elucidate the Li+ transport mechanisms in EC/LiTFSI. II. Molecular Dynamics Simulations Methodology A version of the molecular dynamics simulation package Lucretius8 that includes many-body polarization was used for
10.1021/jp056249q CCC: $33.50 © 2006 American Chemical Society Published on Web 02/15/2006
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TABLE 1: Composition of the Li+ First Solvation Shell
a
temp (K)
no. of EC in a simulation cell, NEC
salt concn (EO:Li)
length of sampling runs (ns)
Oc
313 313 313 313 333 363 363
400 200 400 200 200 200 200
20 20 10 10 10 10 10a
4.0 5.9 3.2 20 20 3 1.5
3.00 3.17 2.68 2.8 2.69 2.78 3.83
no. of oxygen atoms within 2.8 Å of a Li+ O(TFSI-) Oc+O(TFSI-) 0.75 0.67 1.05 0.94 1.05 0.92 0
3.75 3.84 3.73 3.74 3.74 3.7 3.83
Oe 0.50 0.43 0.50 0.48 0.48 0.52 0.36
Dissociated.
all MD simulations. A three-dimensional, periodic cubic simulation cell consisted of 200 or 400 EC molecules and 10 or 20 LiTFSI molecules corresponding to EC:Li ratios of 20 and 10 was utilized. Simulated electrolytes with 200 EC molecules per simulation cell are denoted as small systems, while electrolytes with 400 EC molecules per cell are denoted as large systems. Simulation results for small and large systems will be compared to ensure that reported results are independent of the size of the simulation cell. All electrolytes were created in the gas phase corresponding to a cell (linear) dimension of approximately 8090 Å. The cell size was reduced to yield densities corresponding to an average pressure of 1 atm at each temperature simulated (313, 333, 363, and 393 K for EC:Li ) 10:1 and 313 K for EC:Li ) 20:1). Following equilibration runs of 2-4 ns performed in the NPT ensemble at 1 atm the long sampling runs were performed in the NVT ensemble with the run lengths listed in Table 1. The equilibrated simulation cells had linear dimensions ≈29-38 Å depending on temperature and composition. A Nose-Hoover thermostat and a barostat9 were used to control the temperature and pressure, while bond lengths were constrained using the Shake algorithm.10 The Ewald summation method was used for treatment of long-range electrostatic forces between partial charges and between partial charges and induced dipoles for the many-body polarizable potential. A tapering function was used for scaling the induced dipole-induced dipole interactions to zero at the cutoff of 10 Å, with scaling starting at 9 Å. A multiple time step reversible reference system propagator algorithm was employed,11 with a time step of 0.5 fs for bonding, bending, and torsional motions, a 1.5 fs time step for nonbonded interactions within a 6.5 Å sphere and a 3.0 fs time step for nonbonded interactions between 6.5 and 10.0 Å, and the reciprocal space part of the Ewald summation. Two additional simulations with force fields modified as described below were performed at for the EC:Li ) 10 electrolyte with 200 EC molecules in a box at 363 K for 1.5-2 ns after 1 ns equilibration. In the first simulation, the repulsion between Li+/TFSI- was increased in order to obtain complete salt dissociation. In the second simulation, the Li+/EC short range attraction was increased in order to significantly increase the residence times of EC molecules in the first solvation shell of Li+. III. Structural Properties We begin examination of the structure of the Li+ solvation shell with analysis of the Li+-O radial distribution functions (RDF) shown in Figure 1. Li+ is strongly coordinated by carbonyl oxygen atoms (Oc) from EC and oxygen atoms from TFSI- anions. The position of the first peak of the Li-Oc RDF shown in Figure 1a is at ≈1.95 Å for all concentrations and temperatures investigated. Even the electrolyte with the decreased Li+/TFSI- interactions that resulted in complete ion
Figure 1. Radial distribution functions gLi-O(r) for EC/LiTFSI with 200 EC molecules from MD simulations. Results for EC/LiTFSI simulations using large simulation cell (NEC ) 400) are similar and, therefore, not shown.
dissociation has the same position of the Li-Oc RDF, which is, interestingly, similar to the Li-Oc separation of 1.95 Å found in a quantum chemistry study of the Li+(EC)4 gas-phase cluster.4 Previous simulations of EC/Li+ and EC/LiClO4,2,3 however, reported systematically shorter Li-Oc separations resulting in positions of the first peak of Li-Oc RDF at 1.7-1.8 Å, that is 0.15-0.25 Å closer than found in this work. The magnitude of the first Li-Oc peak is around 25-35, which is about a factor of 2 smaller than the values observed in previous simulations,2-4 thus indicating a significantly less pronounced structuring of the Li+/EC observed in our work compared to previous simulations.2,3 The position and magnitude of the first peak of the Li/ O(TFSI-) RDF almost coincides with those for the Li-Oc RDF, indicating that the free energies of Li+ binding to Oc of EC and O(TFSI-) are comparable in electrolyte solutions. On the other hand, Li+ has a much smaller tendency to be solvated by ether oxygen (Oe) atoms of EC (see Figure 1) compared to other oxygen atom types (Oc and O(TFSI-)) as seen from the LiOe RDF that shows only a small peak at 2.1 Å. A much more pronounced peak of the Li-Oe RDF at 4.05 Å (note the log
LiTFSI Structure and Transport
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Figure 2. Representative snapshots from MD simulations illustrating various compositions of the Li+ first solvation shell. Hydrogen atoms are not shown for clarity.
scale for gLi-O(r) in Figure 1c) corresponds to EC coordinated toward Li+ as shown in a schematic picture in Figure 1b and Figure 2a. The average composition of the Li+ first solvation shell is summarized in Table 1 for EC:Li ) 10 and 20 salt concentrations for small and large simulations cell containing 200 and 400 EC molecules. Li+ is solvated primarily by carbonyl oxygens (Oc) with some contributions from Oe and O(TFSI-). The Li+ coordination by Oc and O(TFSI-) in a small simulation box (NEC ) 200) is similar to its coordination in a large simulation box containing 400 EC molecules (NEC ) 400) as seen from Table 1, thus indicating that the predicted structure of the Li+ coordination is only weakly dependent on the simulation cell with the larger simulation cell leading to each Li+ having 0.1 O(TFSI-) more in its first coordination shell compared to Li+ coordination in a smaller simulation cell. At EO:Li ) 20, each Li+ is coordinated by ≈3.0-3.2 carbonyl oxygen atoms from EC, while in a dissociated electrolyte Li+ has 3.8 carbonyl oxygen atoms from EC in its first solvation shell and often forms structures similar to those
shown in Figure 2a,b. The number of EC molecules coordinating around a Li+ is somewhat less than was found from analysis of Raman spectroscopic studies12 of EC/LiClO4 for salt concentrations from 0.1 to 1 M and conclusions from previous simulations2-4 that indicated four EC present in the Li+ first solvation shell. However, electrospray ionization mass spectroscopy measurements13 of gas-phase Li+ECn clusters found evidence of only Li+EC2 and Li+EC3 clusters and no Li+EC4 clusters. Quantum chemistry studies by Wang et al.14 showed that addition of the fourth EC to the Li+EC3 cluster is favorable only by 2.4 kcal/mol, pointing to the possibility that the Li+EC4 cluster is not very stable in a gas phase, consistent with the electrospray ionization mass spectroscopy measurements.13 We believe that our predictions from our MD simulations of a complete Li+ coordination shell consisting of 3.8 EC molecules on average for the completely dissociated electrolyte mimicking dilute solution conditions are consistent with the results of the above-mentioned quantum chemistry and electrospray ionization mass spectroscopy measurements. For example, if we consider only very tightly bound EC to a Li+ (rLi-Oc < 2.1 Å), we obtain
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Figure 4. Probability of finding n of Li+ within 5 Å of N(TFSI-) and N(TFSI-) with 5 Å of Li+. Separation of 5 Å corresponds to the position of the well after the first peak of Li+‚‚‚N(TFSI-) RDF.
Figure 3. Distribution of angles for molecules in the Li+ first coordination shell for EC:Li ) 10 at 313 K, NEC ) 200.
data showing that Li+ is coordinated by three EC carbonyl oxygens. The Li+ coordination shown in Figure 2b is an example of a Li+ having 4 EC in its complete coordination shell (rLi-Oc
